Depends on what the term "killer asteroid" means. For a once-in-five-hundred-thousand-year civilization destroying asteroids larger than 1 km we have already identified all of them. Possible threats from this population can be projected developing centuries in the future.
For the less extreme threats in the ranges from 100 meters to 1000 meters (which covers impacts in an energy range from 100 megatons to 100,000 megatons) we do have a good way to go, but we are closing in on a 90% detection rate for the larger members of this group.
A 100 meter, 100 megaton asteroid can destroy a city, if it hits it, but is only a localized threat. The large majority of such impactors will cause little or no loss of life since only about 1% of Earth's surface is urbanized. Unless the target is a city the most practical means of dealing with the threat will be local evacuations. For this size a month's warning should be sufficient to deal with the situation. This size can also be completely destroyed by a nuclear explosion, so that a ready-for-launch strategic-sized nuclear warhead could be employed.
A significant fraction of severe threats can never be handled by an Earth-surface survey program - the threat posed by long period comets. This represents as much as 20% of the total threat, but these can only be detected effectively by space-based infrared telescopes, and the warning we will get will only be a couple of years in advance as they approach from the outer reaches of the solar system.